a collaborative space to inspire engaging math instruction for all

How do we invite 6th (and 7th) grade students to authentically engage with an equation in a way that invites students (1) to appreciate how the structure of an equation models a context and (2) to dive deeper in to the meaning of the relationships between variables?

Instead of teaching students how to use the properties of equality to solve “one-step” equations first (which is like using a bazooka to kill a cockroach by the way), I’m wondering if there’s a way to start the exploration of equation solving by inviting students to experience the dynamic relationship between variables first.

Here’s my thinking on one way to do that. I’d love to hear your thoughts so we can get better together.

I hope that there are other 6th (and 7th) grade teachers out there that might find this analysis useful if they are looking for ways to increase student engagement, thinking, and discourse around percents, fractions, and proportional reasoning standards. This engaging learning opportunity can be used at the beginning of a unit as an inquiry-based exploration and pre-assessment. It can also be used as a way of assessing student learning in the middle or the end of a unit. It’s a low-floor opportunity that allows for students at all levels to participate. It also allows for rich discussion and sense-making because solutions can be reached via multiple strategies.

This lesson write-up is for teaching 6th (and 7th) grade proportional reasoning skills (6.RP.1, 6.RP.2, 6.RP.3) using Graham Fletcher’s Rope Jumper lesson. The write-up contains a lesson pathway with specific questions/moves to consider, analysis of the opportunities for student learning, and other wisdoms and insights we learned from teaching this lesson as a part of a lesson inquiry.

Give it a try with your own students. And then tell me how it went. Let’s get better together.